Rheological Behavior of Aqueous Micellar Solutions of a Triblock

A triblock copolymer of ethylene oxide and 1,2-butylene oxide, denoted ... The negative value contrasts with the positive values found for poly(oxyeth...
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2986

Langmuir 2006, 22, 2986-2992

Rheological Behavior of Aqueous Micellar Solutions of a Triblock Copolymer of Ethylene Oxide and 1,2-Butylene Oxide: B10E410B10 Dharmista Mistry,† Tom Annable,‡ Xue-Feng Yuan,§ and Colin Booth*,† School of Chemistry, UniVersity of Manchester, Manchester M13 9PL, United Kingdom, AVecia Ltd, Specialties Research Centre, P.O. Box 42, Hexagon House, Blackley, Manchester M9 8ZS, United Kingdom, and School of Chemical Engineering and Analytical Science, UniVersity of Manchester, Manchester M60 1QD, United Kingdom ReceiVed NoVember 29, 2005. In Final Form: February 2, 2006 A triblock copolymer of ethylene oxide and 1,2-butylene oxide, denoted B10E410B10, was prepared by sequential oxyanionic polymerization and characterized by 13C NMR spectroscopy and gel permeation chromatography. Micellization and the formation of micelle clusters in dilute aqueous solution, the latter a consequence of micelle bridging, was confirmed by dynamic light scattering, and average association numbers of the micelles were determined by static light scattering for T ) 20-40 °C. The frequency dependence of the dynamic storage and loss moduli was investigated for solutions in the range of 5-20 wt %. Comparison with results for poly(oxyethylene) dialkyl ethers (10 wt %, T ) 25 °C) indicated that the viscoelasticity of a copolymer with terminal B10 hydrophobic blocks was roughly equivalent to one with terminal C14 alkyl chains. The temperature dependence of the modulus was investigated for 15 wt % solutions at T ) 5-40 °C. Superposition of the data led, via an Arrhenius plot, to an activation energy for the relaxation process of -40 kJ mol-1. The negative value contrasts with the positive values found for poly(oxyethylene) dialkyl ethers and related HEUR copolymers with urethane-linked terminal alkyl chains. This difference is attributed to the block-length distribution in copolymer B10E410B10, whereby the activation energy of the relaxation process has a positive contribution from the disengagement of B blocks from micelles but a negative contribution from micellization. The negative value of the activation energy for solutions of B10E410B10 was confirmed by determining the temperature dependence of the zero-shear viscosity of its 15 wt % solution.

1. Introduction Poly(oxyethylene)s with hydrophobic end groups are an important class of associative thickeners used for the controlled modification of rheological properties in aqueous systems. Their desirable properties originate from molecular association of the hydrophobic ends of the chains in dilute solution and, above a critical micellization concentration (cmc), from the association of molecules into micelles in which the chains can either loop or extend.1 The bridging of chains between micelles, a dynamic process, leads to the formation of transient micelle clusters and at high enough concentration to the formation of transiently linked networks. The most studied materials, stemming from their commercial importance and compositional simplicity, are modified poly(ethylene glycol)s (HEUR associative thickeners) formed either by reaction with a di-isocyanate followed by an aliphatic alcohol or amine or by a one-step reaction with an alkyl monoisocyanate. Poly(ethylene glycol) dialkyl ethers, prepared using Williamson chemistry in one form or another, provide useful model compounds. References 1-9 provide examples of †

School of Chemistry, University of Manchester. Avecia Ltd. § School of Chemical Engineering and Analytical Science, University of Manchester. ‡

(1) (a) Annable, T.; Buscall, R.; Ettelaie, R., Whittlestone, D. J. Rheol. 1993, 37, 695. (b) Annable, T.; Buscall, R.; Ettelaie, R. Colloids Surf., A 1996, 112, 97. (c) Annable, T.; Buscall, R.; Ettelaie, R. In Amphiphilic Block Copolymers: Self-Assembly and Applications; Alexandridis. P.; Lindman, B., Eds.; Elsevier: Amsterdam, 2000; Chapter 12. (2) Xu, B.; Yetka, A.; Li, L.; Masoumi, Z.; Winnik, M. A. Colloids Surf. A 1996, 112, 239. (3) (a) Kaczmarski, J. P.; Glass, J. E. Langmuir 1994, 10, 3035. (b) May, R.; Kaczmarski, J. P.; Glass, J. E. Macromolecules 1996, 29, 4745. (4) (a) Gourier, C.; Beaudoin, E.; Duval, M.; Sarazin, D.; Maıˆtre, S.; Franc¸ ois, J. J. Colloid Interface Sci. 2000, 230, 41. (b) Beaudoin, E.; Borisov, O.; Lapp, A.; Billon, L.; Hiorns, R. C.; Franc¸ ois, J. Macromolecules 2002, 35, 7436. (5) (a) Pham, Q. T.; Russel, W. B.; Thibeault, J. C.; Lau, W. Macromolecules 1999, 32, 5139. (b) Ming, X.-X.; Russel, W. B. Macromolecules 2005, 38, 593.

the preparation and investigation of these and other types of hydrophobically modified poly(oxyethylene)s. Conventional triblock copolymers with hydrophobic end blocks offer a different synthetic route to associative thickeners with the potential for interesting differences in properties. Of these, triblock poly(oxyalkylene)s have attracted interest, and there are reports of association effects in aqueous solutions of PnEmPn,10-12 BnEmBn,13-23 and SnEmSm24,25 copolymers. We use E to denote (6) (a) Franc¸ ois, J.; Maıˆtre, S.; Rawiso, M.; Sarazin, D.; Beinert, G.; Isel, F. Colloids Surf., A 1996, 112, 251. (b) Beaudoin, E.; Hiorns, R. C.; Borisov, O.; Franc¸ ois, J. Langmuir 2003, 19, 2058. (c) Franc¸ ois, J.; Beaudoin, E. Borisov, O. Langmuir 2003, 19, 10011. (7) Alami, E.; Almgren, M.; Brown, W.; Franc¸ ois, J. Macromolecules 1996, 29, 2229. (8) Chassenieux, C.; Nicolai, T.; Durand, D. Macromolecules 1997, 30, 4952. (9) Mistry, D.; Annable, T.; Booth, C. Abstr., Am. Chem. Soc. 1999, 218, 156. (10) Zhou, Z.-K.; Chu, B. Macromolecules 1994, 27, 2025. (11) Mortensen, K.; Brown, W.; Jørgensen, E. Macromolecules 1994, 27, 5654. (12) Altinok, H.; Yu, G.-E.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C. Langmuir 1997, 13, 5837. (13) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (14) Yang, Z.; Yang, Y.-W.; Zhou, Z.-K.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1996, 92, 257. (15) Zhou, Z.-K.; Chu, B.; Nace, V. M.; Yang, Y.-W.; Booth, C. Macromolecules 1996, 29, 3663. (16) Zhou, Z.-K.; Yang, Y.-W.; Booth, C.; Chu, B. Macromolecules 1996, 29, 8357. (17) Zhou, Z.-K.; Chu, B.; Nace, V. M. Langmuir 1996, 12, 5016. (18) Liu, T.-B.; Zhou, Z.-K.; Wu, C.-H.; Chu, B.; Schneider, D. K.; Nace, V. M. J. Phys. Chem. B 1997, 101, 8808. (19) Liu, T.-B.; Zhou, Z.-K.; Wu, C.-H.; Nace, V. M.; Chu, B. J. Phys. Chem. B 1998, 102, 2875. (20) Kelarakis, A.; Yuan, X.-F.; Mai, S.-M.; Yang, Y.-W.; Booth, C. Phys. Chem. Chem. Phys. 2003, 5, 2628. (21) Kelarakis, A.; Havredaki, V.; Yuan, X.-F.; Yang, Y.-W.; Booth, C. J. Mater. Chem. 2003, 13, 2779. (22) Kelarakis, A.; Ming, X.-T.; Yuan, X.-F.; Booth, C. Langmuir 2004, 20, 2036. (23) Castelletto, V.; Hamley, I. W.; Yuan, X.-F.; Kelarakis, A.; Booth, C. Soft Matter 2005, 1, 138.

10.1021/la0532205 CCC: $33.50 © 2006 American Chemical Society Published on Web 03/04/2006

Rheological BehaVior of Aqueous Micellar Solutions

an oxyethylene unit OCH2CH2, P an oxypropylene unit OCH2CH(CH3), B an oxybutylene unit OCH2CH(CH2CH3), and S an oxyphenylethylene unit OCH2CH(C5H6) originating from the polymerization of styrene oxide. Subscripts m and n denote number-average block lengths in chain units. The range of hydrophobicity is wide: on the basis of values of the critical micelle concentration, the ratio of hydrophobicity for the three chain units mentioned above is P/B/S ) 1:6:12.26,27 The present article is concerned with the aqueous solution properties of one such copolymer with a lengthy central E block: B10E410B10. We used light scattering to confirm association in dilute aqueous solutions of B10E411B10 but principally oscillatory and steady-shear rheometry to characterize the viscoelasticity of the solutions. 2. Experimental Section 2.1. Materials. Copolymer B10E410B10 was prepared by sequential oxyanionic polymerization of ethylene oxide followed by 1,2butylene oxide. The general methods of polymerization and characterization have been described previously.13,14,28 The difunctional initiator was diethylene glycol partially in the form of its potassium salt, mole ratio [OH]/[OK] ≈ 6. The polymerizing mixture was isolated in an ampule by a Teflon tap, and monomer transfer was through a vacuum line, which served to exclude moisture. Ethylene oxide was polymerized for 2 days at 45 °C followed by 5 days at 65 °C before evacuation and addition of butylene oxide, the slower polymerization of which took place at 65 °C (5 days) and 85 °C (10 days). Uniform mixing of the charge of butylene oxide monomer by prolonged shaking with the viscous poly(oxyethylene) melt was uncertain, so the final copolymer was separated in layers as it was taken from the ampule. The sample used was purified by repeatedly dissolving in dichloromethane and adding sufficient hexane to ensure that the copolymer was completely crystallized at low temperature, leaving any poly(oxybutylene), initiated by moisture at the second stage of polymerization, in solution. Both the poly(oxyethylene) precursor and the final copolymer were characterized by 13C NMR spectroscopy (Varian Unity 500, 125.8 MHz, CDCl3 solvent) and gel permeation chromatography (GPC, PLgel columns, N,N-dimethylacetamide eluent at 60 °C, poly(oxyethylene) calibrants). 13C NMR spectroscopy gave absolute values of the block length and composition by comparison of the intensities of resonance of backbone and end-group carbons and also served to verify the block architecture by a comparison of the intensities of the resonance of junction and end carbons. The copolymer composition adopted was calculated from the precursor block length (m ) 411 ( 8) and the overall composition (95.5 ( 0.2 mol % E), leading to n ) 9.7 ( 0.5. In the formula, we round these values to B10E410B10. Corresponding values of the number-average molar mass are 18 100 g mol-1 (E block) and 19 480 (copolymer). GPC gave the distribution width of the copolymer as the ratio of the mass-average to numberaverage molar mass, Mw/Mn ) 1.05 ( 0.01, yielding Mw ≈ 20 500 g mol-1. To place the results for solutions of B10E410B10 in context, we have compared our results with those obtained for more familiar associative thickeners with similar E-block lengths (i.e., a polyurethane-linked polymer (denoted C12UE455UC12) and two dialkyl ethers (denoted C12E455C12 and C16E455C16)). These polymers were prepared in our laboratory from dry PEG20000, the chain length (E455) being checked by end-group analysis based on 13C NMR. The dialkyl ethers were prepared by a modification of the Williamson ether synthesis discussed previously29 and used in our laboratory to (24) Mai, S.-M.; Ludhera, S.; Heatley, F.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1998, 94, 567. (25) Ricardo, N. M. P. S.; Honorato, S. B.; Yang, Z.; Castelletto, V.; Hamley, I. W.; Yuan, X.-F.; Attwood, D.; Booth, C. Langmuir 2004, 20, 4272. (26) Booth, C.; Attwood, D. Macromol. Rapid Commun. 2000, 21, 501. (27) Crothers, M.; Attwood, D.; Collett, J. H.; Yang, Z.; Booth, C.; Taboada, P.; Mosquera, V.; Ricardo, N. M. P. S.; Martini, L. Langmuir 2002, 18, 8685. (28) Heatley, F.; Yu, G.-E.; Sun, W.-B.; Pywell, E. J.; Mobbs, R. H.; Booth, C. Eur. Polym. J. 1990, 26, 583.

Langmuir, Vol. 22, No. 7, 2006 2987 prepare poly(oxyethylene) dialkyl ethers with C1 to C30 end groups.30 The extent of conversion of hydroxyl to ether, determined by IR spectroscopy, was 96%, a value similar to that reported for C12E455C12 prepared by Franc¸ ois and co-workers.7 13C NMR spectroscopy was used to check the formulas, and GPC (as described above) indicated a value of Mw/Mn ) 1.09 ( 0.01 for both copolymers. C12UE455UC12 was prepared by reacting PEG20000 first with isophorone diisocyanate (IPDI) and then with dodecanol, closely following the method described by Emmons and Stevens.31 The extent of conversion of PEG20000 to urethane was 95% (IR and 13C NMR spectroscopy) whereas the reaction of dodecanol with isocyanate end groups was essentially complete. GPC indicated broadening of the distribution, Mw/Mn ≈ 1.3, attributable to limited chain extension in the first stage of reaction. The elution volume at the peak was essentially unchanged, indicating no chain scission during the reaction. The block length of the precursor is conventionally used1-5 to describe polymers of this type, and we do so here. 2.2. Clouding. Clouding temperatures (Tcl) were determined by slowly heating (0.2 °C min-1) solutions of the copolymers, contained in small screw-cap tubes, from 0 to 90 °C. 2.3. Light Scattering. Static light scattering (SLS) intensities from well-filtered dilute solutions (Millipore Millex 0.22 µm filters) were measured by means of a Brookhaven BI200S instrument and vertically polarized incident light of wavelength λ ) 488 nm supplied by an argon-ion laser operated at ca. 500 mW. The intensities of scattered light from sample solutions and water were determined relative to that from benzene. The scattering angle relative to the incident beam was θ ) 90°, and intensities were also measured at 45 and 35° to check the angular dependence of the scattered light intensity. Dynamic light scattering (DLS) measurements were made using the Brookhaven instrument combined with a Brookhaven BI9000A digital correlator. The experimental duration was 10 minutes, and each experiment was repeated at least twice. 2.4. Rheometry. The rheological properties of copolymer solutions were determined using a Bohlin CS50 rheometer with waterbath temperature control. Solutions prepared in small tubes were left to equilibrate for 3 to 4 days before use. A bob-and-cup Couette system was generally used (bob, 14 mm diameter, 21 mm height; cup, 15.4 mm, diameter, 27.4 mm height), but a cone-and-plate was used for solutions of high modulus (cone diameter 40 mm, cone angle 4°). In each case, the gap was set to 0.15 mm. A solvent trap maintained a water-saturated atmosphere to prevent evaporation. Values of the storage and loss moduli (G′ and G′′) were determined for 6-20 wt % copolymer solutions at T ) 25 °C and for 15 wt % solutions at T ) 5-40 °C. A stress sweep served to determine the linear viscoelastic region for each solution. Frequency sweeps (f ) 0.3-20 Hz) were recorded with the rheometer in oscillatory mode, the autostress facility of the Bohlin software being used to limit the strain amplitude (A) to a value within the linear viscoelastic region, A e 1%. This limited measurements of the storage modulus to frequencies at which the autostress feedback was effective at low A (i.e., to solutions of concentrations of 5 wt % or more and to values of G′ greater than ca.0.5 Pa). The viscosities of 15 wt % solutions at T ) 10-40 °C were measured by stepping through selected shear stresses with the instrument in continuous-shear mode. Instrument parameters (integration time, delay time) were optimized to ensure a steady state.

3. Results and Discussion 3.1. Clouding. Clouding temperatures (Tcl) were determined for solutions of copolymer B10E410B10 in the concentration range of 0.1-20 wt %, as shown in Figure 1. Separation into two macroscopic phases was observed in the range c ) 1-10 wt % (29) Cooper, D. R.; Booth, C. Polymer 1977, 18, 164. (30) Cooper, D. R.; Leung, Y. K.; Heatley, F., Booth, C. Polymer 1978, 19, 309. Domszy, R. C.; Mobbs, R. H.; Leung, Y. K.; Heatley, F.; Booth, C. Polymer 1979, 20, 1204. Domszy, R. C.; Mobbs, R. H.; Leung, Y. K.; Heatley, F.; Booth, C. Polymer 1980, 21, 588. (31) Emmons, W. D.; Stevens, T. E. Polyurethane Thickeners in Latex Compositions. U.S. Patent 4,079,028, 1978.

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Mistry et al.

Figure 1. Clouding temperatures of aqueous solutions of copolymer B10E410B10.

at temperatures some 20-30 °C higher than Tcl. Inversion of the tube showed that the solutions with c ) 15-20 wt % were highly viscous at 5 °C, so much so as to be essentially immobile in the test, a preliminary indication of extensive transient network formation at these concentrations. High clouding temperatures coincident with gel formation have been observed in related systems (e.g., aqueous solutions of B12E114B12 and B12E227B1220,22,23). We note that time and frequency scans of dynamic modulus for concentrated solutions of copolymer B12E227B12 at temperatures up to Tcl were consistent with equilibrium states, as would be expected because unimers and micelles are in rapid dynamic equilibrium in micellar systems. For the present rheometric measurements, solution temperatures did not exceed 40 °C (i.e., all solution temperatures were below the minimum clouding temperature). 3.2. Micelles and Micelle Clusters. To confirm the formation of micelles and micelle clusters, a 1 wt % solution of copolymer B10E410B10 was investigated by DLS at T ) 20 °C. The intensitytime correlation function was analyzed by the CONTIN program to give the intensity distribution I(Γ) of decay rate Γ.32 This distribution was converted into the intensity distribution of apparent diffusion coefficient Dapp through Dapp ) Γ/q2 where q ) (4πns/λ)sin(θ/2) is the scattering vector, with ns being the refractive index of the solvent. The Stokes-Einstein equation

rh,app )

kT 6πηDapp

(1)

where k is the Boltzmann constant and η is the viscosity of water at temperature T then gave the intensity distribution of the apparent hydrodynamic radius (i.e., the radius of the hydrodynamically equivalent hard sphere corresponding to Dapp). Normalization gave the intensity fraction distributions. The distribution obtained is the full curve shown in Figure 2. The small particles are assigned to micelles, rh,app ≈ 11 nm, and the large particles are assigned to micelle clusters, rh,app ≈ 60 nm at the peak. The assumption that the scattering is proportional to cM and also that the mass of the scattering units is proportional to the cube of the apparent radius allowed the calculation of the approximate weight distribution of the apparent hydrodynamic radius shown in Figure 2 as a dotted curve. The indication is that 90 wt % of the particles in a c ) 1 wt % solution are single micelles, which, within the assumptions made, is equivalent to 99.9 mol % of the particles. 3.3. Micelle Association Number. Light-scattering measurements were made for solutions of copolymer B10E410B10 with c ) 1 to 9 g dm-3 (i.e., less that 1 wt %) at temperatures of 20, 30, and 40 °C, well below Tcl. To determine the association number by SLS, it is preferable that conditions are chosen such that the copolymer is essentially fully micellized, which means (32) Provencher, S. W. Makromol. Chem. 1979, 180, 201.

Figure 2. Fractional intensity (solid curve) and weight (dotted curve) distributions of the apparent hydrodynamic radius for a 1 wt % aqueous solution of copolymer B10E410B10 at 20 °C. See the text for the assumptions made in deriving the weight distribution function.

Figure 3. Debye plots for aqueous micellar solutions of copolymer B10E410B10 at the temperatures indicated.

that the lowest concentration considered should be at least 10 times the critical micelle concentration (cmc). The cmc of B10E410B10 was not measured, but that of B10E271B10 is reported to be 0.04 g dm-3 at 25 °C.19 The effect of the E-block length on values of the cmc of E/B block copolymers is known to be relatively unimportant compared to that of the B-block length,26 and the effect of temperature on values of the cmc of copolymers with B blocks of 10 repeat units or more is also small.26 Accordingly, we can be sure that values of the cmc of copolymer B10E410B10 in aqueous solution at T ) 20-40 °C are no higher than 0.1 g dm-3. Values of the intensity of light scattered from solution relative to that from benzene (I) and the corresponding relative intensity of light scattered from water (Is) were used to construct the Debye plots shown in Figure 3, in other words, from

K*c 1 ) + 2A2c + ... I - Is Mw,mic

(2)

where c is the concentration in g dm-3, Mw is the weight-average molar mass of the micellar solute, A2 is the second virial coefficient (higher coefficients being neglected in eq 1), and K* is the appropriate optical constant that includes the specific refractive index increment, dn/dc. It is known that dn/dc is insensitive to composition in E/B systems, so the values established in earlier work were used (i.e., 0.135 cm3 g-1 at 20 °C and a temperature coefficient of -2 × 10-4 cm3 g-1 K-1). Other values needed for the calculation were taken from the literature.33 Values of the dissymmetry ratio (scattering intensities I45/I135) were extrapolated to zero concentration and were found to be 1.10 or less, an indication that intraparticle scattering would reduce the value of Mw measured at 90 °C by no more than 7%.34 (33) Johnson, B. L.; Smith, J. In Light Scattering from Polymer Solutions; Huglin, M. B., Ed.; Academic Press: London, 1972; p 29. Gulari, E.; Chu, B. Biopolymers 1979, 18, 2943.

Rheological BehaVior of Aqueous Micellar Solutions

Langmuir, Vol. 22, No. 7, 2006 2989

Figure 4. Frequency dependence of the modulus (A ) 1%) for aqueous solutions of B10E410B10 at 25 °C: (b) G′ and (O) G′′ for the concentrations indicated.

Figure 6. Frequency dependence of the loss modulus (A ) 1%) for 10 wt % aqueous solutions of (b) B10E410B10, (O) C16E455C16, (0) C12E455C12, and (9) C12UE450UC12 at T ) 25 °C.

Figure 5. Concentration dependence of the logarithm of storage (b, G′) and loss (O, G′′) moduli (f ) 1 Hz, A ) 1%) for aqueous solutions of B10E410B10 at 25 °C.

3.4.2. Comparison with ConVentional AssociatiVe Thickeners. In Figure 6, the frequency dependence of the loss modulus determined for a solution of copolymer B10E410B10 is compared with that obtained for solutions of other associative thickeners: C12UE455UC12, C12E455C12, and C16E455C16. The results are for 10 wt % solutions at 25 °C. Values of G′ were lower than those of G′′ for all solutions at all frequencies. As seen in Figure 6 and as observed previously,9 an IPDI linkage has an effect roughly equivalent to extending the end blocks of a dialkyl ether by four methylene units. In this comparison, solutions of B10E410B10 show a rheological response intermediate between those of C12E455C12 and C16E455C16, although there are differences in the detail. Considering the difference in method and the difference in E-block length, the conclusion that a B10 block is equivalent to a C14 block can be considered to be consistent with the ratio of hydrophobicities (C/B ≈ 5:6) deduced previously from values of the cmc for diblock copolymers,26 particularly so since the junction carbon of a C14 block, being adjacent to oxygen, has “oxyethylene” character. For aqueous solutions of several end-capped polymers of type CnUEmUCn, it has been demonstrated that the rheological behavior in the frequency range accessed is governed by a single relaxation time (i.e., it can be modeled by the response of a single Maxwell element1,2,5a,9)

Table 1. Micelle Association Numbers for Aqueous Solutions of Copolymer B10E410B10 T/°C

Nw

A2/10-4 cm3 g-2 mol

20 30 40

7 10 15

1.25 0.48 -0.14

Values of the micelle association numbers, calculated by dividing Mw,mic by the weight-average molar mass of the unimers (19 000 g mol-1, see section 2.1), are listed in Table 1. Also listed are values of A2 calculated from the slopes of the Debye plots. The low values of A2, especially the negative value for solutions at 40 °C, are characteristic of systems in which the copolymer chains form bridges between micelles to a significant extent as concentration is increased.19 Extrapolation to c ) 0 takes the measurement away from the bridging region to reveal the properties of the isolated micelles. A value of Nw ) 25 has been reported for copolymer B10E271B10 in solution at 25 °C,19 compared with about half that value for B10E410B10 (Table 1). A lower value of Nw would be expected for a copolymer with a longer E block, as discussed recently for poly(oxyalkylene)s with a range of compositions and architectures, including BnEmBn copolymers.35 3.4. Dynamic Modulus. 3.4.1. Effect of Concentration. The frequency dependence of the modulus was determined for solutions of copolymer B10E410B10 at 25 °C in the concentration range of 6-20 wt %. Examples are shown in Figure 4: typically values of G′′ exceeded those of G′ over the accessible frequency range. The plot of log(modulus) at f ) 1 Hz against c shown in Figure 5 reinforces this point and indicates an approximately linear dependence on concentration for both moduli. (34) Casassa, E. F. In Polymer Handbook, 3rd ed.: Brandrup, J., Immergut, E. F., Eds.; Wiley: New York, 1989; p 485. Beattie, W. H.; Booth, C. J. Phys. Chem. 1960, 64, 696. (35) Booth, C.; Attwood, D.; Price, C. Phys. Chem. Chem. Phys., submitted for publication.

G′ )

G∞τ2ω2 (1 + τ ω ) 2

2

G′′ )

G∞τω 1 + τ2ω2

(3)

where G∞ is the plateau value of G′ at high frequency, τ is the relaxation time, and ω ) 2πf rad s-1 (f ) frequency in Hz). This is also true for corresponding solutions of dialkyl ethers9 but not for solutions of B10E410B10. We find that at least three Maxwell elements in series are required for even an approximate fit over the frequency range accessed in our experiments; see, for example, Figure 7, where the loss modulus is fitted preferentially. This increase in complexity reflects an important difference in the composition of the alkyl ethers and urethanes compared with that of B10E410B10: the Cn and UCn end groups are strictly uniform in length, whereas the B10 end blocks have a distribution of lengths. Distributions of the relaxation time and high-frequency modulus would be expected. In this respect, we note that a solution prepared by mixing HEUR copolymers with C12, C16, and C20 end blocks does require a combination of three Maxwell elements to fit the frequency dependence of the dynamic moduli, a result consistent with the independent relaxation of the three species.1 3.4.3. Temperature Dependence and ActiVation Energy. The temperature dependence of the modulus was explored for 15 wt % solutions of copolymer B10E410B10 in the range of 5-40 °C. The effect of temperature on the rheology of conventional

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Figure 7. Frequency dependence of the modulus (A ) 1%) for a 15 wt % solution of B10E410B10 at 40 °C: (b) G′ and (O) G′′. The solid curves show the fit to three Maxwell elements in series: G1 ) 2700 Pa, τ1 ) 0.009 s; G2 ) 310 Pa, τ2 ) 0.12 s; and G3 ) 4.5 Pa, τ3 ) 2.0 s. The dotted curves show the fit to a single Maxwell element: G∞ ) 2700 Pa, τ ) 0.0015 s.

Mistry et al.

Figure 9. Superposition showing scaled storage and loss moduli plotted against the scaled frequency. See the caption of Figure 8 for conditions and symbols.

Figure 8. Frequency dependence of the loss modulus (A ) 1%) for 15 wt % solutions of B10E410B10 at temperatures of (O) 5, (b) 10, (0) 15, (9) 20, ()) 25, (() 30, and (3) 40 °C.

associative thickeners is usually explored by finding the best fit of a single Maxwell element to the frequency dependence of the modulus and then analyzing the temperature dependence of the relaxation rate (1/τ) to obtain the activation energy. As discussed above, at least three Maxwell elements are needed to get a realistic fit to the experimental data for the solutions at 40 °C. The results we have for the frequency dependence of the loss modulus across the range of temperatures are illustrated in Figure 8. It is clear from this Figure that the rheological behavior is consistent within the set, and adequate fits to three Maxwell elements in series can be obtained for all (e.g., for the solution at 5 °C, G∞ ) 2000, 100, and 2 Pa and τ ) 0.0014, 0.03, and 0.2 s). However, the range of frequencies available in our experiments precludes an accurate representation of the data in this way, and rather than fit the seven data sets individually, we have used timetemperature superposition with scaling parameters aT (frequency scale) and bT (modulus scale) to combine the data; see Figure 9. The superposition is referenced to T ) 25 °C and best fitted to the loss modulus. The superposition of the data for the storage modulus is less satisfactory, possibly because of the difficulty of measuring low values of G′ while staying within the linear viscoelasticity region (section 2.4). The Arrhenius plot of -log(aT) against 1/T (Figure 10a), which has slope equivalent to a plot of log(relaxation rate) against 1/T, gave E ) -40 kJ mol-1 as an average value over all components of the 15 wt % solution. A similar negative value was obtained using the values of 1/τ obtained for the major component of each three-element fit. Consequently, although there is considerable uncertainty in the magnitude of the activation energy obtained in this way, we can be confident that it is negative. The plot of 1/bT against T shown in Figure 10b indicates an increase in the high-frequency storage modulus with temperature, with the

Figure 10. (a) Arrhenius plot for scaling parameter aT and (b) temperature dependence of 1/bT. The scaling parameters are those used in constructing Figure 9: aT relates to the relaxation time, and 1/bT relates to the high-frequency storage modulus. The data are for 15 wt % aqueous solutions of B10E410B10.

dependence of G′ on T (Kelvin) being very much greater than that predicted by the kinetic theory of network elasticity for a fully formed network. The negative value of the activation energy for the relaxation process (E ) -40 kJ mol-1) found for solutions of B10E410B10 contrasts with positive values (E ) +30 to +70 kJ mol-1) measured for solutions of CnUEmUCn and CnEmCn copolymers.1a,36 That is, the relaxation time for the B10E410B10 solution increases with increasing temperature, whereas the relaxation times for CnUEmUCn and CnEmCn solutions decrease with increasing temperature. As noted in section 3.4.2, as judged by critical micelle concentrations the hydrophobicities of B and C units are similar. Although it is difficult to match copolymers pair by pair, similar endothermic values of the standard enthalpy of micellization (via van’t Hoff plots of log(cmc) against 1/T) for copolymers containing terminal B10 and C12 blocks have been reported (e.g., 23 kJ mol-1 for E18B10,37 30 kJ mol-1 for E24B1038, 40 kJ mol-1 for E8C12,39 and 34 kJ mol-1 for C16E1740). The relation of these (36) Mistry, D. Ph.D. Thesis, University of Manchester, Manchester, U.K., 2000. (37) Kelarakis, A.; Havredaki, V.; Booth, C.; Nace, V. M. Macromolecules 2002, 35, 5591.

Rheological BehaVior of Aqueous Micellar Solutions

values to the unimer-micelle equilibrium constant may not be straightforward,41 but they do correctly define the temperature dependence of the cmc. Accordingly, other things being equal, we might expect similar temperature dependences for other properties of aqueous solutions of CnEmCn and BnEmBn copolymers. An important difference between the two systems, mentioned in section 3.4.2, is the distribution of the hydrophobic-block lengths in B10E410B10. At best, with an ideal polymerization, this will be a Poisson distribution,42 implying, for a B10 block, a range at distribution half-height from B4 to B13. In practice, the distribution may well be wider. A distribution of hydrophobic-block lengths implies a wide temperature range for micellization, with the full associative thickening effect being developed only when the extent of micellization, and consequently the extent of bridging, is high. The activation energy for relaxation in alkyl-ended copolymer solutions is directly related to the process of disengagement of chain ends from micelles, whereas that for B10E410B10 solutions involves both disengagement and micellization. Thus, the overall activation energy involves two processes

Langmuir, Vol. 22, No. 7, 2006 2991

Figure 11. Shear-rate dependence of the steady-shear viscosity of a 15 wt % aqueous solutions of B10E410B10 at 25 °C.

E ) Edis + Emic where Edis is the positive contribution from disengagement and Emic is a negative contribution from micellization, a consequence of the number of copolymer chains in micelles and consequently of the number of chains bridging micelles, increasing with increase in temperature. In the case of the alkyl-ended copolymer solutions, the increase in the extent of micellization is unimportant over the temperature range of interest, and E ) Edis. In the case of B10E410B10 solutions, Emic is the dominant term. The large increase in the high-frequency modulus with increasing T, demonstrated in Figure 10b, is consistent with this explanation (i.e., it is associated with an increase in the extent of micellization and the consequent increase in the extent of bridging). For solutions of alkyl-ended copolymer, CnUEmUCn or CnEmCn, the highfrequency storage modulus is either weakly sensitive to temperature (C16U or C20)1 or falls with increasing temperature (C12U or C16).36 The fall has been ascribed to an increased tendency, as temperature is increased, for the copolymers to loop in a single micelle rather than to bridge between micelles.36 At first sight, it could be thought that there is a contradiction between our assumptions that B10E410B10 is fully micellized at 25 °C in dilute solution (c ) 0.1-1 wt %, see section 3.3) but not in 15 wt % solution. However, it is known43 that the micelleunimer equilibrium changes dramatically when the concentration of copolymer is increased (i.e., when the H-bonded structure of water, and hence the hydrophobic effect that drives micellization,44 is greatly reduced). The effect of mass action is opposed by this reduction in the hydrophobic effect, and in 15 wt % solution, the shorter B blocks are less likely to enter micelles than in 1 wt % solution. Another manifestation of this effect can be seen in the cold gelation (i.e., the formation of a packed-micellar gel on (38) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Heatley, F.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1235. (39) Yeates, S. G.; Craven, J. R.; Mobbs, R. H.; Booth, C. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1865. (40) Barry, B. W.; El Eini, D. I. D. J. Colloid Interface Sci. 1976, 54, 339. (41) Hall, D. G. In Nonionic Surfactants: Physical Chemistry; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; Vol. 23, p 247. (42) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953; p 336. (43) Yu, G.-E.; Deng, Y.-L.; Dalton, S.; Wang, Q.-G.; Attwood, D.; Price, C.; Booth C. J. Chem. Soc., Faraday Trans. 1992, 88, 2537. Nixon, S. K.; Hvidt, S.; Booth, C. J. Colloid Interface Sci. 2004, 280, 219. (44) Tanford, C. The Hydrophobic Effect; Wiley: New York, 1980.

Figure 12. Arrhenius plot of the limiting viscosity at low shear rate for 15 wt % aqueous solutions of B10E410B10.

heating) of solutions of nonbridging diblock EmBn copolymers.45 Cold gelation is not found for solutions of comparable CnEm copolymers with uniform end-blocks.46 3.5. Steady-Shear Viscosity. The observation of a negative activation energy for network relaxation in 15 wt % solutions of B10E410B10 was checked by measuring the dependence of viscosity on the shear rate (γ˘ ) for temperatures in the interval of 10-40 °C. The example shown in Figure 11 for the solution at 25 °C is typical of the temperature range (i.e., almost constant viscosity at γ˘ < 1 s-1 and pronounced shear thinning as γ˘ was increased thereafter). The Arrhenius plot of the zero-shear viscosity (η0, γ˘ ≈ 0.0001 s-1) is shown in Figure 12, where it is seen that the value of η0 increases exponentially with increasing temperature, from 14 to 126 Pa s, with the activation energy being -56 kJ mol-1, a value consistent with that (E ≈ -40 kJ mol-1) obtained from the temperature dependence of the relaxation rate.

4. Concluding Remarks Solutions of copolymer B10E410B10 show rheological characteristics similar to those of the commercially important HEUR copolymers and their poly(oxyethylene) dialkyl ether models. However, an important difference in the molecular structure, derived from the preparation of B10E410B10 by a polymerization process, is the distribution of block lengths in the hydrophobic terminator. In contrast to comparable systems with uniform hydrophobic terminating groups, the extent of micellization becomes an important determinant of the temperature dependence of rheological properties. The effect is to reverse the temperature dependence of the relaxation rate and the high-frequency modulus. (45) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1243. (46) Ameri, M.: Attwood, D.; Collett, J. H.; Booth, C. J. Chem. Soc., Faraday Trans. 1997, 93, 2545.

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Acknowledgment. We thank Dr. S.-M. Mai and Dr. W. Mingvanish for help with the preparation of the copolymer. Copolymer synthesis at Manchester was funded by EPSRC. In particular, D.M. is grateful for an EPSRC CASE studentship

Mistry et al.

financed in cooperation with Zeneca Specialties. We also thank our referees for several suggestions that improved the presentation of our article. LA0532205